Flexible Shipping - Tax settings
For shipping methods made with Flexible Shipping plugin taxes work exactly the same as for flat rate shipping methods. If you enable taxes in your store, you will have to enter the shipping price without the tax.
Enable shipping taxes in WooCommerce
To enable shipping taxes, you first have to enable tax rates and calculations option in WooCommerce settings ( WooCommerce > Settings > General).
After that, you will be able to enter the Tax settings in the WooCommerce. There you can set the tax class for shipping.
Tax Status in Flexible Shipping method
You can also enable or disable tax for certain Flexible Shipping methods. Inside Flexible Shipping method settings you can set Tax Status.
You can set it as Taxable and use taxes for this shipping method, or set it as None and disable taxes for it.
Additional cost and Taxes
If you set Additional cost based on price in Flexible Shipping rules, it will be added based on shipping price with the tax. Shipping tax is added by WooCommerce after all rules calculation.